Block #84,972

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 4:02:52 AM · Difficulty 9.2801 · 6,718,694 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

92237911af63a64b130db055c4a7c7e23067c79b61f0f0b4028c44750bf861cc

View on Chainz ↗

Height

#84,972

Difficulty

9.280136

Transactions

Size

207 B

Version

Bits

0947b6ff

Nonce

21,284

Timestamp

7/27/2013, 4:02:52 AM

Confirmations

6,718,694

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

be5587a44e825ce80f1221a2fdcac392466fbff15811c7015c5bcece55db7294

Transactions (1)

Coinbasebe5587a44e825c…5bcece55db7294

1 in → 1 out11.5900 XPM109 B

AdhmaJ1p…MhFRDjQ7

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.273 × 10¹¹⁴(115-digit number)

62738898771929075170…22220819764390983849

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

6.273 × 10¹¹⁴(115-digit number)

62738898771929075170…22220819764390983849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.273 × 10¹¹⁴(115-digit number)

62738898771929075170…22220819764390983851

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.254 × 10¹¹⁵(116-digit number)

12547779754385815034…44441639528781967699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.254 × 10¹¹⁵(116-digit number)

12547779754385815034…44441639528781967701

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.509 × 10¹¹⁵(116-digit number)

25095559508771630068…88883279057563935399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.509 × 10¹¹⁵(116-digit number)

25095559508771630068…88883279057563935401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.019 × 10¹¹⁵(116-digit number)

50191119017543260136…77766558115127870799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.019 × 10¹¹⁵(116-digit number)

50191119017543260136…77766558115127870801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.003 × 10¹¹⁶(117-digit number)

10038223803508652027…55533116230255741599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.003 × 10¹¹⁶(117-digit number)

10038223803508652027…55533116230255741601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer